Not exactly, though the "00" is perfectly correct as the last two digits of 1800. The numbering started each year for each manufacturer at 1 (no leading zeros), then went to 9999, then to 1a -9999a, 1b - 9999b and so on. The suffix letter does not indicate the year, it is part of the serial number. The year of manufacture is on the receiver ring (1941 in this case), the maker on the front toggle. (byf was one of several codes assigned to Mauser at different times.)
The 8.88 is the bore size in millimeters as determined by a plug gauge. For 9mm, that will usually range from 8.80 to 8.88mm. Bore gauging was an important part of barrel manufacture and that mark was put on along with the barrel proof (small proof mark) when the barrel was made, not after it was installed. I have no idea why there would be two bore sizes unless the barrel was re-gauged for some reason.